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The process of normalization consists
of shifting the fraction left until the
high-order hexadecimal digit is nonzero
and reducing the characteristic by the
number of hexadecimal digits shifted.
A
zero fraction cannot be normalized, and
its associated characteristic therefore
remains unchanged when normalization is
called for.
Normalization usually takes place
when the intermediate arithmetic result
is changed to the final result.
This
function is called postnormalization.
In performing multiplication and divi-
sion, the operands are normalized before
the arithmetic process.
This fUnction
is called prenormalization.
Floating-point addition and subtrac-
tion may be performed with or without
normalization.
When an operation is performed with-
out normalization, high-order zeros in
the result fraction are not eliminated.
The result mayor may not be normalized,
depending on the original operands.
In both normalized and unnormalized
operations, the initial operands need
not be in normalized form.
Floating-Point Addition and Subtraction.
Addition or subtraction of two floating-
point numbers consists of characteristic
comparison and fraction addition.
The
characteristics of the two operands are
compared, and the fraction with the
smaller characteristic is right shifted.
its characteristic is increased by one
for every hexadecimal digit shift (four
binary places), until the two
characteristics agree.
The fractions
are then added algebraically to form an
intermediate sum.
Subtraction differs
here only in that the sign of the second
operand is inverted before fraction
addition.
Normalization may be called for in
either addition or subtraction. Normal-
ization consists of shifting the frac-
tion left and decreasing the charac-
teristic one for every hexadecimal digit
shift.
Floating-Point Multiply and Divide
The multiplication of two floating-point
numbers consists of a characteristic
addition and a fraction multiplication.
1-30
The sum of the characteristics less 64
is used as the characteristic of an
intermediate product.
The product fraction is normalized by
prenormalizing the operands before the
operation, and postnormalizing the
intermediate result if necessary.
Division of two floating-point num-
bers consists of subtracting the charac-
teristics and dividing the fractions.
The difference between the dividend and
divisor characteristics plus 64 is used
as an intermediate characteristic.
The quotient fraction is normalized
by prenormalizing the operands before
the operation.
Postnormalizing the
intermediate quotient is never
necessary.
Instruction Format
Floating-point instructions use the
following two formats:
RR Format
r--------T------T------,
lOp Code
I
R1
I
R2
I
l _______
- i _____ - i ______ J
o
7 8
11 12
15
RX Format
r--------T------T------T--~---T--------,
lOp Code
I
R1
1
X 2
I
B2
I
D2
I
l -_______
~
_____
i ______
~
_____ i ________ J
o
7 8
11
12
15
16
19
20
31
In these formats, R1 deSignates the
address of a floating-point register.
The contents of this register will be
called the first operand.
The second
operand location is defined differently
for two formats.
In the RR format, the R2 field speci-
fies the address of a floating-point
register containing the second operand.
The same register may be specified for
the first and second operand.
In the RX format, the contents of the
general register specified by X 2 and B2
are added to the content of the D2 field
to form an address designating the loca-
tion of the second operand.
A zero in an X 2 or B2 field indicates
the absence of the corresponding address
component.
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